Launch a specific iphone app when docking in home made dock? How doable is this?

I'm doing a project to build myself a quality ipad speaker cabinet dock (because the ones to buy are aither not good enough or too costly), and had an idea for a feature that would be cool, but I have no idea how I could implement it.

I want to incorporate and old school 80s/90s type LED spectrum analyser in it for display, ie this sort of thing:


Now I could buy the one shown in that video for about $130 plus postage but I can't really afford to pay out money like that for a bit of bling.

I've got an iphone app called Audio LED which gives the same kind of display based on sound through the mic, and I'm wondering if I added a second dock for the phone (the dock is for the ipad but could easily have room for the phone too. It'd make sense if this project could actually house and charge them both) if there's a way of linking this app to audio output from the dock?

Probably sounds confusing sorry, but to clarify, if the ipad and iphone are both in the dock cabinet then playing music from the dock would automatically launch the spectrum analyser app on the phone.  That's what I want but it it probably well beyond my means without a lot of advice.

I know that docks can trigger certain behaviour in the phones, so they clearly are sending a message to the phone when it docks (eg with the "iLuv" branded docks you get a message on the phone asking if you want to download their app when you dock the phone). So this certainly seems doable because to do this the phone must 'know' it is attached to a specific brand of dock in order to prompt the download.  That means the dock is sending info to the phone to tell it this, and that's what I want to somehow replicate, but with commands instead that tell it to launch this Audio LED app.

Ie logic something along the lines of:

      Phonestatus == Docked &
      Musicplaying == Yes

Probably pie in the sky really, but I'm certain in theory it's doable - it's just whether it's realistically doable for me.

There's a much easier alternative that involves the likes of one of these really cool and cheap LCD displays:

You program them via a parallel cable I think using software like LCDsmartie, and people have used them for exactly what I want, but the problem is that means it being connected to a PC, and that kind of rules these out in this case alas. 

Anyone savvy with the sort of stuff that'd be needed to do this please pipe up now, or if it's really dreaming then by all means say so.
I've got some basics electronics knowledge and even used to make my own PCBs and stuff when I was a kid but only really know a few basics.  I've got stuff like breadboard and a various components etc and am happy to meddle but I'm guessing this would require programming of some kind of chip to store the commands, and knowledge of how the code distinguishes one app from another to identify the right one.

Alternative suggestions welcome on how I could have a pretty looking spectrum analyser without spending tons of cash. If money was no object I'd just buy one of those ones I linked to at the top, but that's far from being the case!!!